Thieves' Town/No Logic
Getting there
Thieves' Town has some convenient ways in from the light world that do not require the Moon Pearl.
With a bottle, you can perform a subtile YBA in the interior door of the secret passage where your uncle was, to reach the TT basement in cave state. The door you need to perform the YBA in is deep, so you won't be able to see yourself in it.
If you have the Master Sword or better, it will have one stationary pixel at its tip that you can see in the wall when holding it out sideways, and you can make sure that this pixel is at the edge of the 2px black border. With the Fighter Sword, you need to infer your position from the moving sparkles as you hold out your sword -- the topmost pixel should spend a fair amount of time sparkling.
The stationary pixel at the tip of the Master Sword is on the highest possible pixel.
Drink a red or green potion at the moment you enter the door transition to reach this room of Thieves' Town.
Getting around
The only barrier to progress you might face is the big key door. If you use the YBA above to enter in cave state, you can freely unlock that door from the back.
The back of the big key door acts as a small key door, so if you came from another dungeon (such as Desert Palace (NL)), remember that unlocking that door will use up a key.
If you reached TT from the light world, it can be useful to walk out the front door to reach the Village of Outcasts in the Fake Dark World.
Where you can go
You can clip out of bounds in this corner of the Thieves' Town attic to enter Desert Palace (NL). Clip into the wall to reach a down-teleport position (I used a Citrus Clip, but there's probably a bomb setup), and buffer down+left.
This clip is allowed in Major Glitches logic, and it may be the first access to Desert Palace (NL) in a glitched inverted seed.
The position from which you can down-teleport.
Press down+left simultaneously to enter Desert Palace (NL).
A subtile YBA can take you to the dark room in Eastern Palace.
Getting the crystal
You may want to bring Blind to the boss room with the shining light and then not fight her, especially if you're in cave state. If you perform the LSD Blind glitch at the start of the fight, you'll be able to leave the room. Later, you can re-enter in Thieves' Town state and Blind will still be there.
You can also kill Blind in cave state and re-enter later to claim the crystal.